Solve Complex Fraction Division: 15/3 ÷ (12/8 ÷ (1⅘ ÷ 8))

$\frac{15}{3}:(\frac{12}{8}:(1\frac{4}{5}:8))=\text{?}$

We solve the first fraction exercise:

$\frac{15}{3}=5$

We solve the second fraction by breaking it down into smaller multiplication exercises:

$\frac{12}{8}=\frac{4\times3}{4\times2}=\frac{3}{2}$

We convert the third fraction into a simple fraction:

$1\frac{4}{5}=\frac{9}{5}$

Now we obtain the exercise:

$5:(\frac{3}{2}:(\frac{9}{5}:8))=$

We note in inner parentheses the division exercise, a multiplication exercise between fractions:

$5:(\frac{3}{2}:(\frac{9}{5}\times\frac{1}{8}))=$

$5:(\frac{3}{2}:\frac{9}{5\times8})=$

Now we invert the fraction to create a multiplication exercise:

$5:(\frac{3}{2}\times\frac{5\times8}{9})=$

We combine the multiplication exercises, since it's just a multiplication operation:

$5:\frac{3\times5\times8}{2\times9}=$

Now we invert the fraction to create a multiplication exercise:

$5\times\frac{2\times9}{3\times5\times8}=$

We add the 5 to the numerator of the fraction in the multiplication exercise:

$\frac{5\times2\times9}{3\times5\times8}=$

We simplify the 5 in the numerator and denominator:

$\frac{2\times9}{3\times8}=$

We break down the 8 into a smaller multiplication exercise:

$\frac{2\times9}{3\times2\times4}=$

We simplify the 2 in the numerator and denominator:

$\frac{9}{3\times4}=$

We break down the 9 into a smaller multiplication exercise:

$\frac{3\times3}{3\times4}=$

We simplify the 3 in the numerator and denominator:

$\frac{3}{4}$